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# converting this degree measure to radians?

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I have to convert $${-14.8°}$$ into radians, expressing my answer as exact values and as approximate measures (to the nearest hundredth of a radian).

This may be a very elementary question, but I'm not sure how express my answer in exact values?

I got $${-7.4 \over 90}π$$ using the conversion factor of $${π \over 180°}$$ and dividing $${-14.8°}$$ and $${180°​​}$$by 2.

However, the textbook got $${-37π \over 450}$$ . That means $${2.5}$$ was used to multiply $${-14.8°}$$ and $${180°​​}$$ . Why 2.5? How did the textbook get this number?

Thank you! :)

Dec 3, 2018

#1
+99377
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I have to convert -14.8 degrees into radians, expressing my answer as exact values and as approximate measures (to the nearest hundredth of a radian).

$$\text{Not that the surtitle c is a symbol for radians. (not commonly used though)}\\180^\circ=\pi^c\\ 1^\circ=\frac{\pi^c}{180}\\ -14.8^\circ=\frac{-14.8\pi^c}{180}\\ -14.8^\circ=\frac{-148\pi^c}{1800}\\ -14.8^\circ=\frac{-37\pi}{450}\;\;radians\\$$

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Dec 3, 2018

#1
+99377
+2
$$\text{Not that the surtitle c is a symbol for radians. (not commonly used though)}\\180^\circ=\pi^c\\ 1^\circ=\frac{\pi^c}{180}\\ -14.8^\circ=\frac{-14.8\pi^c}{180}\\ -14.8^\circ=\frac{-148\pi^c}{1800}\\ -14.8^\circ=\frac{-37\pi}{450}\;\;radians\\$$